ME495 Lab 07 Hydrostatic Force

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San Diego State University *

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495

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Mechanical Engineering

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Apr 3, 2024

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Hydrostatic Force ME 495: Mechanical and Thermal Systems Lab Section 05: Thursday Group D Authors: Soeung Khanitha, Smith Emilee, Sichantha Jack, Taylor Charles Instructor: Dr. Hamid Nourollahi Thursday, February 22, 2024

1 Table of Contents Objective of Experiment ( Khanitha Soeung ) .......................................................................................... 2 Equations and Symbols (Emilee Smith) ..................................................................................................... 2 Equipment ( Khanitha Soeung ) ................................................................................................................. 3 Experimental Setup ( Khanitha Soeung, Jack Sichantha) ....................................................................... 4 Experimental Procedure ( Khanitha Soeung ) ........................................................................................... 4 Experimental Results (Emilee Smith) ........................................................................................................ 5 Discussion of Results (Charles Taylor) ....................................................................................................... 7 Lab Guide Questions .................................................................................................................................... 9 Conclusion (Jack Sichantha) ....................................................................................................................... 9 References ( Khanitha Soeung ) .................................................................................................................. 9 Appendix ( Jack Sichantha) ...................................................................................................................... 10 List of Tables Table 1: Symbols ............................................................................................................................................ 2 Table 2: Equations .......................................................................................................................................... 3 List of Figures Figure 1: Diagram of Hydrostatic Pressure Apparatus .................................................................................. 4 Figure 2: Depth vs Mass Plot ......................................................................................................................... 5 Figure 3: Plot of Depth of Pressure (Experimental and Theoretical) vs Mass ............................................... 5 Figure 4: Plot of Moment (Experimental and Theoretical) vs Mass .............................................................. 6

2 Objective of Experiment ( Khanitha Soeung ) This experiment is designed with two primary objectives. The first objective is to investigate the hydrostatic thrust exerted on a plane surface submerged in water under the varying degrees of submersion, both partial and full. The second objective is to determine the precise position of the line of action of this thrust and compare it against the theoretical expectations. In order to facilitate this investigation, the F1-10 Hydraulics Bench and F1-12 Hydrostatic Pressure Apparatus, developed by Armfield Limited in Ringwald, Hampshire, England are utilized. The team hypothesizes that the hydrostatic force will increase in direct proportion to the depth of the submersion. Furthermore, the team anticipates that the experimental determination of the line of action of the force will closely correspond to the theoretical predictions. Therefore confirming the fundamental principles governing hydrostatic force. Equations and Symbols (Emilee Smith) Table 1: Symbols Symbol Definition/Units Units D Height of end face (m) Meter (m) B Width of end face (m) Meter (m) L Length of arm (m) Meter (m) H Height of pivot (m) Meter (m) d Depth of water from base of quadrant (m) Meter (m) F Hydrostatic Thrust (N) Newton (N) m Mass (kg) Kilogram (kg) g Acceleration due to gravity Meters per Second Squared (m/s^2) w Weight Newton (N) A Area (m^2) Square Meter (m^2)

3 M Moment (Nm) Meter (m) h Mean depth of immersion (m) Meter (m) h’ Depth of the center of pressure (m) Meter (m) h” Distance of center of pressure below the pivot Meter (m) Table 2: Equations Equation 1: Hydrostatic Thrust (partially submerged) 𝐹 = ρ𝑔?ℎ = (1/2)ρ𝑔?? 2 Equation 2: Experimental Depth of Pressure (partially submerged) ℎ" = (2𝑚?)/(ρ?? 2 ) Equation 3: Theoretical Depth of Pressure (partially submerged) ℎ" = 𝐻 − (?/3) Equation 4: Hydrostatic Thrust (fully submerged) 𝐹 = ρ𝑔?𝐷(? − (𝐷/2)) Equation 5: Experimental Depth of Pressure (fully submerged) ℎ" = (𝑚?)/(ρ?𝐷(? − (𝐷/2))) Equation 6: Theoretical Depth of Pressure (fully submerged) ℎ" = 𝐷 2 12 +(?−?/2) 2 ?−𝐷/2 + 𝐻 − ? Equation 7: Moment ? = 𝐹ℎ” Equipment ( Khanitha Soeung ) ● Armfield Limited F1-10 Hydraulics Bench ○ Facilitates experiments in fluid mechanics and hydraulics ● Armfield Limited F1-12 Hydrostatic Pressure Apparatus ○ Facilitates the measurement and analysis of hydrostatic forces on submerged surfaces ● Various weights ○ Used to increase and decrease the hanging mass of the balance arm. Multiple masses from 10 grams to 100 grams.

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